migration assistant - from Mac Mini to iMac

I just bought an iMac running Snow Leopard.
I wish to migrate all my data (apps, e-mails, docs) from my previous Mac Mini running Tiger to the iMac.
I try using the migration assistant without firewire cable (through a direct ethernet cable or through a WiFi LAN).
I get as far as entering the code generated by the iMac on the Mini, but then the Mini asks for the code a second time and after a few seconds starts searching for other computers while the iMac waits with preparing the data.
If I go back on the iMac, it generates a new code which the Mini detects and allows to enter it but the loop described above starts again.

On the Mini, the OS is X.4.11 and the migration assistant is version 1.0.6 (101.1).
The iMac is running X.6.2 and migration assistant version 3.0 (318).

I'm in the exact same situation.
I was told earlier by Apple support to run software upgrade on both. The G4 was up to date. The new G5 required a 2 hour download of upgrades that are now complete, but it didn't solve the problem.
I was also told that I may have to get a firewire cable. He didn't know of any reason why the ethernet connection wouldn't work perfectly, but clearly it isn't. That requires a trip into town tomorrow.
He also suggested that upgrading my older mac to 10.5 could be helpful. This is not available from Apple. It is only available as media shipped from third party suppliers online (I found a supplier for $16 plus $10 shipping, but I'll make sure other options don't work first. I fear that the OS upgrade will render some external devices useless)

The next thing I will try is to copy my G4 hard drive onto my external hard drive and then try to migrate from that. (This will take many hours, but I'll do the copy overnight) I'll keep you posted on my success or failure.